Applied to study of surface reactions
\[ \ce{CO2 + 4H2 -> CH4 + 2H2O} \]
\(\ce{Rh/CeO2}\) catalyst
Previous study

Had access to an in situ reaction chamber for FT-IR
… as well as mass flow controllers and rapid cross-over switch valves to build a gas system with
Wanted to easily remove spectators and noise, and estimate a sequence of events.
Had heard of a technique called Phase sensitive detection…
Enhances a signal of a certain frequency (\(k\omega\)) and phase (\(\varphi\))
\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]
\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]
In essence, a cross-correlation between sampled data (\(f(t)\)) and modulating signal (\(g(t)\)). \[ (f*g)(\tau) := \int^{t_0+T}_{t0} \overline{f(t)} g(t + \tau) \mathrm{d}t \]
\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]
Figure: Animated illustration of a cross-correlation. Source: https://en.wikipedia.org/wiki/Cross-correlation
\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]
Lags in time: (0.0, -29.0, 60.5, 30.0) s
Lags in phase: (0.0, -1.52, 3.17, 1.57) rad
We have the following reaction system (\(\ast\) is adsorption site)
\[ \begin{align} \ce{A (g) + \ast &-> A^\ast}\\ \ce{B (g) + \ast &-> A^\ast}\\ \ce{AB^{\ast} + B^\ast &-> AB2^{\ast} + \ast}\\ \ce{AB2^{\ast} + B^\ast &-> AB3^{\ast} + \ast}\\ \ce{AB3^\ast &-> AB3 (g) + \ast}\\ \end{align} \]
We will disturb the system by varying \(\ce{B (g)}\) as a sine
We measure the signals corresponding to the intermediates
The order: \(\varphi{(\ce{B^\ast})} < \varphi{(\ce{AB^\ast})} < \varphi{(\ce{AB2^\ast})} < \varphi{(\ce{AB3^\ast})}\)
But first, building time
Figure: Demodulated phase spectra (half period) of T = 60 s experiment. Catalysts 2020, 10(6), 601; https://doi.org/10.3390/catal10060601
As we want the lags (\(\varphi\)), we need to solve \(\phi_k^\text{PSD}\)
\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]
Figure: Demodulated phase spectra of T = 60 s experiment with maximum amplitude (line) for each individual wavenumber and some phase lags (dots). Catalysts 2020, 10(6), 601; https://doi.org/10.3390/catal10060601
I got:
Further developments on the system lead to:
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